Lisans ve lisansüstü TMD yaz kampı Şirince’de Matematik Köyü’nde 13 Temmuz – 30 Ağustos 2009 tarihleri arasında gerçekleşecektir. Değişikliğe tabi olabilecek ders programını aşağıda bulacaksınız.
Bu yaz yapılacak lisans yaz kampları için TÜBİTAK’tan ne yazık ki destek alınamamıştır.
Bir matematik bölümünün birinci sınıfını başarıyla bitirmiş her öğrenci yaz kampına katılabilir; matematik bölümü dışından gelecekler ancak istisnai olarak ve yer varsa kabul edileceklerdir.
2009 TMD Yaz Kampı başvuru formu icin tıklayın. Başvuru formunu aslicankorkmaz@nesinvakfi.org adresine e-postayla yollamalısınız. Başvurunuzun ulaştığına dair bir onay mesajı gönderilecektir. Katılmak istediğiniz tarihleri başvuru formuna mutlaka yazmalısınız.
Yaz kampının ücreti, dört öğün yemek, konaklama, dersler ve her türlü temel ihtiyaçlar dahil kurumlara 70 TL, kişilere 50 TL`dir. Çadırlarda kalacaklara %50 indirim uygulanır. İhtiyacı olanlara burs vermekte imkânlarımız dahilinde cömert davranıyoruz.
Süre: Katılım hafta sayısına göredir. Haftalar pazartesi sabahı başlar ve bir sonraki pazar akşamı biter. Köy‘e başlangıç tarihinden bir gün önce (bir pazar günü) gelinir ve bitiş tarihinde (gene bir pazar günü) Köy‘den ayrılınır. Haftalarımızda altı çalışma gün vardır, hafta ortasında, perşembe günü tatil yapılır ve topluca bir yere gidilir.
Her ders 1,5 ile 2 saat arasında sürer. Genelde günde en az dört ders vardır. Aynı anda birkaç ders birden olabilir. Katılımcıların da seminer vermesi beklenir. Bazı dersler İngilizce olabilir; dolayısıyla katılımcıların matematik kitabı okuyacak ve ders dinleyebilecek kadar İngilizce bildikleri varsayılır.
Köy‘de bol bol çadır kuracak yer vardır. Kısıtlı sayıda çadırımız vardır ancak çadırda kalacak katılımcıların çoğunun çadırlarını getireceklerini umuyoruz.
Katılımcıların Köy‘de çamaşır, bulaşık, temizlik, yemek gibi gündelik işlerde çalışacakları varsayılır.
Title: Abelian Group Theory
Instructor: Prof. Dr. Ali Nesin
Institution: İstanbul Bilgi Üniversitesi
Prerequisites: –
Dates: 13-26 July
Contents: Classification of finitely generated abelian groups. Torsion abelian groups. Free abelian groups and their subgroups. Classification of divisible abelian groups. Automorphisms of abelian groups.
Başlık: Analizden Kesitler
Eğitmen: Prof. Dr. Yusuf Ünlü
Kurum: Çukurova Üniversitesi
Gereken: En az bir yıllık analiz dersi
Tarih: 13-19 Temmuz
İçerik:
Analizin sayılar teorisine bazı uygulamaları
Sonsuz seriler.
Faktöriyel ve Gamma fonksiyonu
Title: Mathematical Foundations of Quantum Mechanics
Instructor: Msc. E. Mehmet Kıral
Institution: Boğaziçi Üniversitesi
Prerequisites: Lineer Algebra
Dates: 13-19 July
Contents: In this short one week course we will not do quantum mechanics, but rather cover the mathematical background necessary for having a formal theory of it. So we will cover the theory of Hilbert Spaces with a view towards its use in Physics. We will accomplish this by following John Von Neumanns book; “Mathematical Foundations of Quantum Mechanics”.
Title: Classical Mechanics
Instructor: Dr. Ashna Sen
Institution: Brockwood Park School
Prerequisites: Lisans
Dates: 13-26 July
Contents:
Day 1: Introduction to classical mechanics short history. Basic concepts of force, motion, mass and units of physical quantities used in laws of motion. Quick survey of laws of motion.
Day 2. Set up of all three laws of motion and introduction to Newton`s Laws. Implications of Newton`s laws, idea of inertial frame of reference and motion as momentum. Examination of F = p¢ (derivative of momentum) and third law: F(ij) = –F(ji). Full analysis of all three laws of motion and some problems related to them including motion down an inclined plane and some Tension/String/Pulley type problems
Day 3: Introduction of conservation of energy. F = ma continued, Concept of work as an integral quantity. F.dr = dW and integrating around integrals with one example using vector calculus and study of line integrals/paths of integration.
Day 4 &5: Continue with definition of work as line integral and conservative fields meaning of conservative and non-conservative force fields. How the definition of work arises out of integrating T = mv2. Also, around a closed curve the line integral gives zero` signifying a conservative field. Examples and several line integral problems worked out showing path independence.
Day 6&7: Curl of a conservative force field is zero. Why? Proof. Idea of potential, and potential energy of a force field and their difference. Motion in a general one dimensional potential including calculations of stability and equilibrium.
Day 8 More on momentum. Conservation of momentum. Angular momentum revisited. Some examples using vector calculus.
Day 9 Calculus of variations introduction to famous problems like the `Brachistochrone`. Fermat`s principle and use of it for proofs of Snell`s law and problems arising out of them. Motivation: idea behind `extremalising`
Day 10 Lagrange`s formulation introduction: Principle of least action. Changing coordinate systems Setting up for Hamiltonian dynamics. Suggestions and more equations. Generalised momenta, Conditional variation including the lagrange multiplier method catenary. What is the meaning of constraint.
Day 11&12 More indepth analysis of Hamiltonian and Lagrangian ideas and wrap-up of all concepts.
Title: Random Graphs
Instructor: Dr. Özlem Beyarslan
Institution: Boğaziçi Üniversitesi
Prerequisites: –
Dates: 13-26 July
Contents:
1. What is a random graph G(n, p).
2. First order theories.
3. Zero-one laws.
4. Ehrenfeucht games
5. What happens in G(n, p) when p is irrational.
Title: Real Closed Fields
Instructor: MSc. Demirhan Tunç
Institution: University of Notre Dame
Prerequisites: Some basic notions about fields and polynomial rings
Dates: 20-26 July
Content: Ordered Fields, Formally Real Fields, Real Closed Fields and Hilberts 17th Problem.
Başlık: Hilbert`s 16th Problem
Eğitmen: Dr. Nermin Salepçi Ferret
Kurum: Koç Üniversitesi
Gereken: Giriş seviyesi projektif geometri
Tarih: 20-26 Temmuz
İçerik: Reel projektif yüzey üzerindeki reel cebirsel eğrilerin topolojik özelliklerinin incelenmesi ve derecesi 6 ve daha küçük olan reel cebirsel eğrilerin sınıflandırılması.
Title: Polynomials
Instructor: Mr. Doğa Güçtenkorkmaz
Institution: İstanbul Bilgi Üniversitesi
Prerequisites: At least one year of solid mathematics education.
Dates: 20-26 July
Contents: Algebraic properties of polynomials, irreducibility of some polynomials, field extensions and Galois groups.
Başlık: Morse Kuramı
Eğitmen: Dr. Ferit Öztürk
Kurum: Boğaziçi Üniversitesi
Gereken: İleri düzeyde analiz
Tarih: 20 Temmuz – 2 Ağustos
İçerik: Her manifoldun üzerinde bir “morse fonksiyonu” vardır. Bu fonksiyonun kritik noktaları ve bunların çevresi, manifoldun topolojisini anlamak için yeterlidir.
Başlık: Analitik Sayılar Teorisinde Üreteç Fonksiyonları
Eğitmen: Msc. Ayhan Dil
Kurum: Akdeniz Üniversitesi
Gereken: Temel Calculus kavramlarını bilmek.
Tarih: 27 Temmuz – 2 Ağustos
İçerik: Toplamlar ve rekürans bağıntıları. Sayılar teorisi ve kombinatorikteki bazı özel polinomlar ve sayılar hakkında temel bilgiler, bunların özelliklerinin üreteç fonksiyonları yardımıyla incelenmesi.
Title: Ordinals, Cardinals and Zorn`s Lemma
Instructor: Prof. Dr. Ali Nesin
Institution: İstanbul Bilgi Üniversitesi
Prerequisites: None (or almost none)
Dates: 27 July – 9 August
Contents: Ordinaller, kardinaller, Yerleştirme Aksiyomu, Seçim Aksiyomu, Zorn Önsavi ve uygulamaları.
Title: Introduction to Probability Theory
Instructor: Msc. Elif Yamangil
Institution: Harvard University
Prerequisites: Calculus with one variable and some familiarity with calculus with several (two) variables.
Dates: 27 July – 2 August
Content:
Title: Hyperbolic Manifolds
Instructor: MSc. Özgür Evren
Institution: CUNY
Prerequisites: Advanced.
Dates: 3-9 August
Content: Hiperbolik Uzayin Tanimi (Ust Yari Uzay ve Birim Kure modelleri), Jeodezikler, Hiperbolik Uzaklik Fonksiyonu ve Hiperbolik Alan, Izometrilerin Siniflandirilmasi ve Isometri Gruplari, Duzgun Sureksiz Grup Etkileri, Ayrik Altgruplar, Yorunge Uzaylari, Hiperbolik Yuzey Ornekleri ve Poincare Teoremi.
Title: A Mathematical Introduction to Modal Logic
Instructor: MSc. Can Başkent
Institution: CUNY
Prerequisites: Good level of abstract mathematics + mathematical maturity.
Dates: 10-16 August
Content: Introduction: Motivations and History. Syntax, Semantics and Proof Theory of Modal Logic. Topological and Game Theoretical Semantics. Truth Preserving Operations and Bisimulations. Completeness proofs. Different Modal Logics and corresponding defining formulae. Applications of Modal logics to philosophy and computer science.
Title: Around Sylow Theory
Instructor: Prof. Dr. İsmail Güloğlu
Institution: Doğuş Üniversitesi
Prerequisites: At least one year of good undergraduate math education and the following concepts and results from group theory will be assumed as known (better as mastered): Group, subgroup ,coset, Lagrange`s Theorem, normal subgroup, homomorphism, kernel of a homomorphism, isomorphism, automorphism, quotient group, isomorphism theorems ,direct product, structure theorems for finite abelian groups, basic knowledge about permutations (sign, cycle decomposition.etc.) and symmetric group, Cayley`s theorem of abstract algebra.
Dates: 3-9 August
Content:
Title: Elementary Mathematics from a Higher Point of View
Instructor: Prof. Dr. Alexandre Borovik
Institution: Manchester University
Prerequisites: None (or almost none)
Dates: 3-23 August
Content: Why is teaching mathematics so difficult? My course will be devoted to hidden structures and concepts of elementary mathematics which frequently remain unnoticed but seriously influence students perception of mathematics.
I will try to develop some (time permitting) of the following themes.
1. Arithmetic of “named” numbers, like the problem of dividing 10 apples between 5 people; Laurent polynomial ring; dimensional analysis in physics, from Froudes Law of Steamship Comparison to Kolmogorovs “5/3 Law” for the energy distribution in turbulent flow.
2. Why is addition commutative? I will analise a real life story about a girl aged 6 who could easily solve “put a number in the box” problems of the type 7 + [ ] = 12, by counting how many 1`s she had to add to 7 in order to get 12 but struggled with [ ] + 6 = 11, because she did not know where to start.
3. What is common and what is difference between induction and recursion?
4. Carry (remember what is it? According to Wikipedia, “carry is a digit that is transferred from one column of digits to another column of more significant digits” during addition of decimals) and cohomology. 10-adic and 2-adic numbers. Eulers sum
1 + 2 + 4 + 8 + 16 + … = -1.
5. “Russian peasants multiplication” and modules over commutative rings; exponentiation in modular arithmetic; its applications to cryptography: Diffie-Hellman key exchange and RSA; timing and power trace attacks on embedded cryptographis devices (like microchips in credit cards). Mathematics of binary trees.
6. Why are the Chinese Remainder Theorem in Number Theory and the Lagrange Interpolation Formula in Numerical analysis one and the same thing?
At least the beginning of the course will be relatively elementary. But the students in the course should be psychologically prepared for sudden jumps onto very abstract levels of mathematics.
Title: Groups and Geometry
Instructor: Assoc. Prof. Ayşe Berkman
Institution: ODTÜ / METU
Prerequisites: At least one year of mathematical education
Dates: 10-16 August
Content: There are multiple connections between geometry and group theory, since geometry means symmetry and the properties of symmetries are studied by group theory. In this short course we will exploit this idea, from tilings and freezes to Coxeter groups (some of which can be considered to be the building structures of our universe!)
Title: Nonstandard Analysis
Instructor: Assoc. Prof. David Pierce
Institution: ODTÜ / METU
Prerequisites: Some knowledge of analysis and abstract algebra.
Dates: 10-16 Ağustos
Content: Invented in the 17th century if not earlier, calculus can be understood in terms of “infinitesimals“: Non-zero numbers whose absolute values are less than every fraction 1/n. In this understanding, the region bounded by a curve is the sum of rectangles of infinitesimal width; the slope of a curve at a point is a ratio of infinitesimals. But there are no infinitesimals on the so-called “real number line”. In the usual “rigorous” treatment of calculus, invented in the 19th century, infinitesimals do not appear: they are replaced with the notion of a “limit”.However, 20th-century logic shows that infinitesimals can be made just as “real” as the real numbers, so that the original intuitive approach to calculus is entirely justified.
Title: Elliptic Curves
Instructor: Asst. Prof. Ayhan Günaydın
Institution: Oxford University
Prerequisites: At least two years of good undergraduate math education
Dates: 10-16 August
Content: Elliptic curves lie in the meeting point of three main areas of mathematics: arithmetic, geometry and complex analysis. The primary aim of this short course is to understand how these areas are connected via elliptic curves. We shall follow a very historical path to do this; we start by considering things as done by Gauss, Abel and Jacobi, and end up at working with elliptic curves in the framework of modern language of geometry and arithmetic. A more precise list of topics would be as follows:
1. Elliptic integrals and elliptic functions: basic definitions, inversion of elliptic functions by Gauss and Abel, the Weierstrass function, Abels theorem.
2. Modular groups and modular functions.
3. Imaginary quadratic fields.
4. Arithmetic of elliptic curves.
We shall mostly focus on 1 and 3. If time allows some more advanced topics might be considered as well.
The audience will be assumed to be familiar with basic notions of algebraic geometry and manifold theory; and of course a good two semesters of complex analysis. A good source for this course would be “Elliptic Curves, H. McKean – V. Moll, Cambridge University Press, 1997”.
Title: Discrete Valuation Rings
Instructor: Prof. Dr. Ali Nesin
Institution: İstanbul Bilgi Üniversitesi
Prerequisites: Abstract algebra, some basic knowledge of ring and field theory
Dates: 10-16 August
Content: Generalities. Discrete valuation rings and their maximal ideals. Valuations on ℚ. Archimedean and non-Archimedean valuations. Dedekind domains. Localization. Power series, meromorphic functions, p-adic numbers and their extensions. Integral closure. Completion. Derivations. More if time allows.
Title: Short Course in Complex Analysis
Instructor: Prof. Eduard Emelyanov
Institution: ODTÜ / METU
Prerequisites: Analysis
Dates: 24-30 August
Content: This course is devoted to a short presentation of basic ideas of geometric theory of functions of one complex variable including the Riemann theorem.
Title: Special Functions: Orthogonal Polynomials
Instructor: Dr. Veronica Pillwein
Institution: RISC, Linz
Prerequisites: Basic knowledge in calculus and algebra.
Dates: 17-23 August
Content: Certainly one of the most prominent members in the class of Special Functions are orthogonal polynomials like Jacobi, Hermite or Laguerre polynomials. These polynomials gained their fame because of their various applications in, e.g., physics, numerical mathematics and chaos theory. One can take different viewpoints in the investigation of orthogonal polynomials: (complex) analytic, combinatorial, symbolic, …
In this course we will give a self-contained introduction to the theory of orthogonal polynomials covering several of the above aspects. It will contain the basic facts about orthogonal polynomials and provide an outlook to further interesting topics in this context which go beyond the scope of this course. Those interested in symbolic summation and corresponding RISC software will find that the methods treated in the lecture of Flavia Stan are applicable to various problems discussed in this course.
As prerequisites it will be sufficient to have basic knowledge in calculus and algebra.
Title: Topics in Computer Algebra
Instructor: Msc. Burçin Eröcal
Institution: RISC, Linz
Prerequisites: Linear algebra and some abstract algebra
Dates: 17-23 August
Content: After introducing some tools from computer algebra such as computing in homomorphic images and p-adic lifting, applications of these methods to obtain asymptotically fast algorithms for exact linear algebra over polynomial rings will be presented. We will use the open source computer algebra system Sage (http://sagemath.org) for demonstrations of the algorithms discussed.
Title: Symbolic Summation
Instructor: MSc. Flavia Stan
Institution: RISC, Linz
Prerequisites: Basic knowledge from analysis and linear algebra.
Dates: 17-23 August
Content: Many of the topics discussed in the lecture can be found in the book “Concrete Mathematics – A Foundation for Computer Science“ by R.L.Graham, D.E.Knuth und O.Patashnik (Addison-Wesley, 1994). A citation from its preface:
“… But what exactly is Concrete Mathematics? It is a blend of CONtinuous and disCRETE mathematics. More concretely, it is the controlled manipulation of mathematical formulae, using a collection of techniques for solving problems. Once you dots have learned the material in this book, all you will need is a cool head, a large sheet of paper, and a fairly decent handwriting in order to evaluate horrendous looking sums, to solve complex recurrence relations, …“
The main topics of the lecture are: recurrence relations, generating functions and summation algorithms. These methods have a wide applicability e.g. in dealing with special functions like classical orthogonal polynomials (more details in Veronika Pillweins course).
Moreover, out of enviromental reasons and to eliminate the “decent handwriting“ factor, we will present implementations of these techniques in different software packages of the Algorithmic Combinatorics group at RISC such as fastZeil, MultiSum, GeneratingFunctions, … and illustrate how these programs are useful in a mathematicians day-to-day life.
Title: Finite Rings
Instructor: Prof. Oleg Belegradek
Institution: İstanbul Bilgi Üniversitesi
Prerequisites: Some abstract algebra
Dates: 24-30 August
Content: Finite simple rings will be classified.
Başlık: Analizden Kesitler
Eğitmen: Prof. Dr. Ali Nesin
Kurum: İstanbul Bilgi Üniversitesi
Gereken: En az bir yıl matematik eğitimi almış olmak.
Tarih: 24-30 Ağustos
İçerik: Gama fonksiyonları, Liouvill sayıları ve analizden seçme konular.
Title: Philosophy of Mathematics
Instructor: BSc. Brian Edwards
Institution: Brockwood Park School
Prerequisites: Interest in philosophy and mathematics
Dates: 13-26 July
Content:
Part 1Ancient Greek Foundations of Philosophy and Mathematics
1. Introduction + Journey to Pythagorean Revolution
2. Pythagorean specifics: Form, Cosmos, Harmonics
3. Platonic developments: Geometry as Virtue: Academy
4. Plato`s problem: Being and Time
5. Aristotle: Being ta mathematikos and University foundations.
6. The Euclidean Point: Summary
Part 2Modern Transformations of Ancient Problems
1. Cosmos to Nature, Euclid to Galileo
2. Renaissance synthesis: Bruno, Cusanus, and Infinity
3. The rigorous Form: Bacon, Newton and Locke
4. The Cartesian explosion of Doubt
5. Ratio and Mathematics: Kant, Leibniz, Spinoza
6. Back Home: Mathematics, Philosophy and the 20th century.
This is obviously ambitious for two weeks. The course is thematic, so it may morph depending on the group and where the reflection naturally leads us.
Title: Evrende Neler Var?
Instructor: Prof. Dr. Ali Alpar
Institution: Sabancı Üniversitesi
Prerequisites: None!
Dates: 17-23 Ağustos
Content: Gözlemsel olarak evrenin yapısı hakkında bildiklerimiz ve bunun arkasındaki fizik ve bilim tarihi.
Title: Engin Mermut
Instructor: Yard. Doç. Dr. Engin Mermut
Institution: Dokuz Eylül Üniversitesi
Prerequisies: An introductory course on algebra is enough. Familiarity wih modules and rings, some special rings, exact sequences will be useful.
Dates: 17-23 Agust
İçerik: This one week short course is an introductory course on homological algebra and aims to do as much of the main parts for the following fundamental topics.
1. Motivation: algebraic topology and presentations, projective (free) resolutions.
2. The adjoint pair of functors Hom and tensor product in the categories of modules.
3. Projective, injective and flat modules. Purity.
4. Homology of complexes of modules.
5. Projective, injective and flat resolutions.
6. Derived functors.
7. Ext and Tor, the derived functors of Hom and tensor product.
8. Projective dimension, injective dimension, flat dimension of modules.
9. The left global dimension, the right global dimension, the weak dimension of a ring.
10. Ext and extensions: the Baer sum of short exact sequences.
11. Some special rings characterized homologically: Semisimple rings, von Neumann regular rings, hereditary rings and Dedekind domains, semihereditary rings and Prüfer domains, …
12. Further topics if time permits.
Title: Commutative Algebra
Instructor: Doç. Dr. Feza Arslan
Institution: ODTÜ
Prerequisites: Herhangi bir temel cebir dersi almış olmak. Ring, ideal gibi kavramlara biraz aşina olmak.
Dates: 24-30 Ağustos
Content: Modules, Rings and modules of fractions, Primary decomposition, Integral dependence and integral closure. (Some examples from algebraic geometry and algebraic number theory will be the central objects of interest throughout the course.)
Title: Injective Modules
Instructor: MSc. Sinem Odabaşı
Institution: Dokuz Eylül Ü.
Prerequisites: Modüller kategorisine aşina olmak.
Dates: 10-16 Ağustos
Content:
Injective modules
Divisibility
Essential extensions
Injective envelope
Indecomposable injective modules
Injective modules and chain conditions